jachyra
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f(x) = (2x^3 + 4x^2 - x + 1) / (-x^2 - x + 2)
The limit of this function as x approaches infinity is the oblique asymptote f(x) = -2x - 2
This can be verified by performing long division with the two polynomials to get:
f(x) = -2x -2 + (x +5)/(-x^2 - x + 2)
as x -> infinity, the term (x +5)/(-x^2 - x + 2) -> zero
Now my question is why does the following not work:
f(x) = (2x^3 + 4x^2 - x + 1)/(-x^2 - x + 2) * (1/x^2)/(1/x^2)
f(x) = (2x + 4 - 1/x + 1/x^2) / (-1 - 1/x + 2/x^2)
lim f(x) as x -> infinity should then be -2x - 4 because all other terms approach zero as x gets larger and larger right?
why is this wrong? I am so confused... I thought the answers should have been the same!
The limit of this function as x approaches infinity is the oblique asymptote f(x) = -2x - 2
This can be verified by performing long division with the two polynomials to get:
f(x) = -2x -2 + (x +5)/(-x^2 - x + 2)
as x -> infinity, the term (x +5)/(-x^2 - x + 2) -> zero
Now my question is why does the following not work:
f(x) = (2x^3 + 4x^2 - x + 1)/(-x^2 - x + 2) * (1/x^2)/(1/x^2)
f(x) = (2x + 4 - 1/x + 1/x^2) / (-1 - 1/x + 2/x^2)
lim f(x) as x -> infinity should then be -2x - 4 because all other terms approach zero as x gets larger and larger right?
why is this wrong? I am so confused... I thought the answers should have been the same!